messages
listlengths 1
1
| ground_truth
stringclasses 104
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[8, 0, 2, -12, -10, -4],\n [0, -7, -1, 0, 8, -4],\n [0, 0, 7, -2, -3, 9],\n [0, 0, 0, 10, 8, 14],\n [0, 0, 0, 0, 4, -8],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[10, 11, 0, 1, -1, -13],\n [0, -7, 5, -4, 10, -1],\n [0, 0, 15, 2, 4, -4],\n [0, 0, 0, 0, 7, 0],\n [0, 0, 0, 0, 14, -13],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
50
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[6, -2, 9, 11, -8, 3],\n [-2, 13, -1, 10, 3, 2],\n [9, -1, -2, -1, 2, 10],\n [11, 10, -1, -10, 4, -9],\n [-8, 3, 2, 4, -12, 8],\n [3, 2, 10, -9, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[7, -4, -10, 5, -6, 10],\n [-4, 1, 1, 9, 3, 8],\n [-10, 1, -3, 1, 4, 2],\n [5, 9, 1, -10, 0, -8],\n [-6, 3, 4, 0, -15, 2],\n [10, 8, 2, -8, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-4, 3, 12, 2, 10, -10],\n [3, 13, 3, 2, 4, 4],\n [12, 3, -9, 0, -2, -5],\n [2, 2, 0, 7, 11, -6],\n [10, 4, -2, 11, 6, 0],\n [-10, 4, -5, -6, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-6, 6, -6, 5, -1, 1],\n [0, -10, -13, -3, 0, -8],\n [0, 0, 1, 1, 6, 10],\n [0, 0, 0, 1, 0, -2],\n [0, 0, 0, 0, -2, -1],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-3, 1, 15, 5, 8, -13],\n [0, -10, -11, 6, 10, 1],\n [0, 0, -14, 10, -1, -11],\n [0, 0, 0, -10, 11, 2],\n [0, 0, 0, 0, -2, -2],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[15, -5, -1, -4, -13, 1],\n [0, 3, 4, -12, -13, 10],\n [0, 0, -8, 8, 13, 13],\n [0, 0, 0, 2, -15, -13],\n [0, 0, 0, 0, -2, -11],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
38
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[11, 0, 12, 0, 14, -12],\n [0, 10, 12, -3, -14, 15],\n [0, 0, -8, 8, -1, -5],\n [0, 0, 0, -3, -14, -8],\n [0, 0, 0, 0, -9, -6],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-10, 2, 2, -11, 5, 13],\n [0, 12, -14, -5, 14, -3],\n [0, 0, 14, -10, 8, 10],\n [0, 0, 0, -12, 13, 7],\n [0, 0, 0, 0, -8, 10],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
56
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[8, 3, 4, -13, 0, -6],\n [3, 1, -4, 10, -8, 6],\n [4, -4, -11, -4, 2, -7],\n [-13, 10, -4, 4, 8, 4],\n [0, -8, 2, 8, -6, -8],\n [-6, 6, -7, 4, -8, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[2, -2, 8, -5, -4, 7],\n [-2, 3, 10, 4, -8, 7],\n [8, 10, 14, 4, 10, -10],\n [-5, 4, 4, -1, 4, 2],\n [-4, -8, 10, 4, 10, 6],\n [7, 7, -10, 2, 6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[4, -2, -4, -6, -6, 2],\n [-2, 5, 3, 4, 0, -4],\n [-4, 3, 14, -4, -1, 0],\n [-6, 4, -4, 11, -9, 4],\n [-6, 0, -1, -9, 5, 4],\n [2, -4, 0, 4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
65
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-1, -1, 0, -6, -4, 12],\n [0, -12, -9, 6, -14, 10],\n [0, 0, 11, -1, 15, -8],\n [0, 0, 0, 7, -2, 15],\n [0, 0, 0, 0, 14, -5],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[5, 2, 2, 4, -6, -4],\n [2, 6, 10, 2, -2, -7],\n [2, 10, 0, 5, -9, -8],\n [4, 2, 5, 13, -6, 9],\n [-6, -2, -9, -6, -2, -4],\n [-4, -7, -8, 9, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
73
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[7, 10, 1, 6, 11, -11],\n [10, -12, -4, -4, -6, -2],\n [1, -4, -12, 6, 2, -3],\n [6, -4, 6, -5, 9, 4],\n [11, -6, 2, 9, 4, 1],\n [-11, -2, -3, 4, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-10, -2, 3, -6, 1, -1],\n [-2, -12, 8, 8, -8, 9],\n [3, 8, -5, -8, 10, 12],\n [-6, 8, -8, -14, -6, -10],\n [1, -8, 10, -6, -12, 6],\n [-1, 9, 12, -10, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[13, 13, 6, 10, 6, -6],\n [13, 4, -2, 0, -4, 4],\n [6, -2, 0, -2, -7, 3],\n [10, 0, -2, 8, -12, -2],\n [6, -4, -7, -12, 10, -8],\n [-6, 4, 3, -2, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[12, -12, 1, 4, 8, -10],\n [-12, -14, 2, 2, -6, 4],\n [1, 2, -5, -10, 4, 0],\n [4, 2, -10, -4, -14, 4],\n [8, -6, 4, -14, 1, 2],\n [-10, 4, 0, 4, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
99
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[12, 0, 4, 0, 2, -5],\n [0, -15, -2, 8, -4, -1],\n [4, -2, -11, 5, -7, -5],\n [0, 8, 5, 2, 2, 4],\n [2, -4, -7, 2, 9, -2],\n [-5, -1, -5, 4, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
75
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-6, 10, -3, -1, 8, -8],\n [10, -14, -4, -6, 8, -7],\n [-3, -4, 11, 0, 14, 4],\n [-1, -6, 0, -1, -6, -11],\n [8, 8, 14, -6, 8, 4],\n [-8, -7, 4, -11, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
104
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-2, -12, 12, -10, -4, -2],\n [-12, -12, -2, -8, 6, -7],\n [12, -2, 13, -12, 2, 7],\n [-10, -8, -12, 4, 6, -9],\n [-4, 6, 2, 6, 0, 7],\n [-2, -7, 7, -9, 7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-9, 8, -2, -6, 0, -2],\n [8, -3, 3, -3, 10, -12],\n [-2, 3, -4, -6, -8, 6],\n [-6, -3, -6, -11, 4, 13],\n [0, 10, -8, 4, -2, -7],\n [-2, -12, 6, 13, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[12, 3, -2, 6, 14, 7],\n [0, -3, 11, 4, -13, -11],\n [0, 0, -10, 15, 9, 15],\n [0, 0, 0, -11, 12, 11],\n [0, 0, 0, 0, 4, -4],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-5, 8, 6, 7, -8, -8],\n [8, -2, -7, -12, 1, 3],\n [6, -7, -15, -4, -1, 8],\n [7, -12, -4, 13, -6, 0],\n [-8, 1, -1, -6, -11, 8],\n [-8, 3, 8, 0, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-9, -12, 3, 6, 3, -10],\n [0, -3, -5, -3, -3, 12],\n [0, 0, 12, 4, -1, 5],\n [0, 0, 0, 3, -8, 4],\n [0, 0, 0, 0, 3, 10],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[8, 3, 0, -9, 3, -4],\n [0, 15, 7, -2, -5, 10],\n [0, 0, -5, -10, -14, -5],\n [0, 0, 0, 4, -10, 1],\n [0, 0, 0, 0, -8, -8],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
49
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-5, 0, 9, -2, 9, -6],\n [0, -10, -6, -4, 0, 0],\n [9, -6, -2, 7, 7, 5],\n [-2, -4, 7, 13, -3, 0],\n [9, 0, 7, -3, -5, 6],\n [-6, 0, 5, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-7, 1, 5, -3, 0, 5],\n [1, -1, 6, 12, 12, 7],\n [5, 6, -15, 0, 1, 4],\n [-3, 12, 0, 1, 0, 2],\n [0, 12, 1, 0, -3, -6],\n [5, 7, 4, 2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
74
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[11, -6, 3, 8, 8, 11],\n [-6, 7, 6, -8, -2, -4],\n [3, 6, 1, -4, -10, -9],\n [8, -8, -4, 13, -6, -4],\n [8, -2, -10, -6, -4, -4],\n [11, -4, -9, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
79
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[6, 10, -12, -15, -9, 14],\n [0, -7, 13, -13, -8, 13],\n [0, 0, -12, 2, 4, 11],\n [0, 0, 0, 9, 2, 12],\n [0, 0, 0, 0, -1, 11],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[0, -2, 10, 0, -9, -7],\n [0, 14, 14, 6, -5, -14],\n [0, 0, 14, -12, 2, 10],\n [0, 0, 0, 13, -15, 15],\n [0, 0, 0, 0, -3, -10],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
47
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-11, 2, 15, 14, -11, 14],\n [0, -6, -15, -6, -11, -4],\n [0, 0, 11, -9, -7, 6],\n [0, 0, 0, 13, -15, -5],\n [0, 0, 0, 0, 4, -9],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
54
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-5, -6, -8, 2, -10, 8],\n [-6, -4, 11, 12, 2, 3],\n [-8, 11, 2, -3, 5, -7],\n [2, 12, -3, -14, 2, 15],\n [-10, 2, 5, 2, 9, 2],\n [8, 3, -7, 15, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
102
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[12, 11, -2, 8, -6, -10],\n [11, -3, 6, -6, 5, -10],\n [-2, 6, 11, -8, 2, -6],\n [8, -6, -8, 13, 12, -1],\n [-6, 5, 2, 12, 13, -6],\n [-10, -10, -6, -1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[13, 6, -13, -10, -2, -4],\n [6, 4, -2, -6, 6, -1],\n [-13, -2, -8, 0, -4, 2],\n [-10, -6, 0, 12, -2, 2],\n [-2, 6, -4, -2, -9, -4],\n [-4, -1, 2, 2, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-4, -12, 2, -4, -5, 6],\n [-12, 8, 1, 1, 0, -4],\n [2, 1, 12, -1, -6, -2],\n [-4, 1, -1, 9, 1, -4],\n [-5, 0, -6, 1, 9, 7],\n [6, -4, -2, -4, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
72
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[11, 12, 15, 9, 12, 3],\n [0, 11, -1, -7, -8, 4],\n [0, 0, -12, -2, 9, -14],\n [0, 0, 0, -8, -10, 0],\n [0, 0, 0, 0, -3, -3],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
46
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[2, -8, -4, -1, -3, -2],\n [-8, 15, 2, 2, -4, 4],\n [-4, 2, 7, 2, 6, -4],\n [-1, 2, 2, -2, -4, 6],\n [-3, -4, 6, -4, -15, 6],\n [-2, 4, -4, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
66
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[3, 7, 0, -3, 1, 9],\n [7, 11, -1, -6, 4, 6],\n [0, -1, 14, 8, 2, 11],\n [-3, -6, 8, -13, 0, 0],\n [1, 4, 2, 0, 12, -4],\n [9, 6, 11, 0, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-3, 2, -8, -4, 4, -1],\n [2, 5, -2, -6, 6, 8],\n [-8, -2, -10, 7, 1, 9],\n [-4, -6, 7, 14, -9, -4],\n [4, 6, 1, -9, 5, 2],\n [-1, 8, 9, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[8, -3, 5, -2, 2, 3],\n [-3, 2, -4, 7, 9, -4],\n [5, -4, 5, -6, 6, 14],\n [-2, 7, -6, 0, -7, -5],\n [2, 9, 6, -7, 6, -4],\n [3, -4, 14, -5, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[10, 2, -7, -10, -5, 9],\n [0, -10, -10, -3, -5, -2],\n [0, 0, -13, 7, 5, -13],\n [0, 0, 0, 2, 1, 4],\n [0, 0, 0, 0, 14, -15],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-5, -6, 6, -7, -14, 12],\n [-6, 7, -2, 4, 4, -2],\n [6, -2, -15, -5, 8, -11],\n [-7, 4, -5, -8, 2, 1],\n [-14, 4, 8, 2, -10, 0],\n [12, -2, -11, 1, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[15, -2, 4, 6, 4, -4],\n [-2, 12, 4, -2, 0, -2],\n [4, 4, -12, 12, 0, -4],\n [6, -2, 12, -12, 2, 1],\n [4, 0, 0, 2, -11, 3],\n [-4, -2, -4, 1, 3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
86
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[13, 5, 2, -10, 2, 1],\n [5, 15, -4, -10, -8, -4],\n [2, -4, -7, 14, 0, 0],\n [-10, -10, 14, -6, -7, -10],\n [2, -8, 0, -7, -6, -1],\n [1, -4, 0, -10, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[8, 8, -2, -2, 0, -1],\n [8, 7, 10, -3, 4, -4],\n [-2, 10, 15, 8, 12, -6],\n [-2, -3, 8, 1, -6, -2],\n [0, 4, 12, -6, 12, -10],\n [-1, -4, -6, -2, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-5, 8, 2, -8, 3, 4],\n [8, 12, 6, 10, -6, 12],\n [2, 6, -7, -12, -6, 4],\n [-8, 10, -12, 7, -6, 0],\n [3, -6, -6, -6, 14, 4],\n [4, 12, 4, 0, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
103
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[3, -2, -4, 1, 7, 0],\n [-2, -6, 6, 12, 3, 4],\n [-4, 6, -6, -6, -2, 12],\n [1, 12, -6, 7, -4, 8],\n [7, 3, -2, -4, -2, 11],\n [0, 4, 12, 8, 11, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
31
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[12, -5, -7, -5, -1, -7],\n [-5, 10, 7, 6, 10, -2],\n [-7, 7, 11, 2, 9, 8],\n [-5, 6, 2, -9, -8, -8],\n [-1, 10, 9, -8, 8, 6],\n [-7, -2, 8, -8, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
87
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-8, -10, 3, -14, -1, 0],\n [-10, -9, -5, -2, -4, 12],\n [3, -5, 5, -11, -4, 1],\n [-14, -2, -11, 11, 8, 2],\n [-1, -4, -4, 8, -13, 1],\n [0, 12, 1, 2, 1, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[0, 13, 13, 15, 15, 1],\n [0, 8, 4, 7, 2, 2],\n [0, 0, 2, -1, -1, -10],\n [0, 0, 0, -12, 7, -8],\n [0, 0, 0, 0, -3, -7],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[1, -4, -4, -2, 0, 6],\n [-4, -2, 0, 2, -6, 8],\n [-4, 0, 13, 2, 2, 8],\n [-2, 2, 2, -8, 4, 6],\n [0, -6, 2, 4, 9, 10],\n [6, 8, 8, 6, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
71
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[6, -13, -11, 0, 2, 10],\n [0, -5, 1, 0, 10, 7],\n [0, 0, 5, -9, -14, 14],\n [0, 0, 0, 9, -11, -11],\n [0, 0, 0, 0, -11, -8],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
43
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[-5, -12, 6, 6, 6, -14],\n [0, 13, -10, 11, -2, -15],\n [0, 0, -15, 15, -15, -15],\n [0, 0, 0, 13, 2, 11],\n [0, 0, 0, 0, -6, -7],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-14, 4, 2, -2, 11, 0],\n [4, -3, -2, 0, 8, 2],\n [2, -2, -5, -4, 0, -2],\n [-2, 0, -4, 7, 8, -2],\n [11, 8, 0, 8, -12, -11],\n [0, 2, -2, -2, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-10, 6, 10, -15, -12, -2],\n [0, 4, 2, -5, 13, 5],\n [0, 0, -7, 11, -1, -4],\n [0, 0, 0, 3, -10, 4],\n [0, 0, 0, 0, -15, 6],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[6, 14, 12, -4, 11, -7],\n [14, 14, 13, 10, -2, 1],\n [12, 13, 3, 4, -8, -3],\n [-4, 10, 4, 0, 0, 6],\n [11, -2, -8, 0, 7, -2],\n [-7, 1, -3, 6, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[7, 2, 0, 0, -4, -12],\n [2, 13, -13, 4, -2, 4],\n [0, -13, -15, 2, -2, 3],\n [0, 4, 2, -4, 6, 7],\n [-4, -2, -2, 6, 12, -3],\n [-12, 4, 3, 7, -3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[7, -5, -3, 4, -2, 0],\n [-5, -14, -1, 5, -10, 4],\n [-3, -1, -9, 2, -5, -8],\n [4, 5, 2, -11, -10, -4],\n [-2, -10, -5, -10, 6, 0],\n [0, 4, -8, -4, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
81
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-3, -12, 3, -2, 5, 5],\n [-12, -1, -8, 12, 8, -2],\n [3, -8, -3, -4, 0, -2],\n [-2, 12, -4, 7, 8, -8],\n [5, 8, 0, 8, 0, -8],\n [5, -2, -2, -8, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[13, -14, -15, -7, -7, 7],\n [0, -13, 10, 15, 2, -5],\n [0, 0, -15, 13, -2, 4],\n [0, 0, 0, -9, 10, -14],\n [0, 0, 0, 0, 12, 1],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
68
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[3, 5, 5, -4, 0, 4],\n [5, 11, 11, -1, 6, 0],\n [5, 11, -14, 7, -1, 1],\n [-4, -1, 7, 9, -4, 4],\n [0, 6, -1, -4, -5, 0],\n [4, 0, 1, 4, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-7, -3, 8, -8, -2, 8],\n [0, 1, 8, -11, 9, -14],\n [0, 0, 14, 8, -7, -12],\n [0, 0, 0, 2, 0, 14],\n [0, 0, 0, 0, 5, 2],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[2, -2, 8, 6, -6, 0],\n [-2, 1, -10, -2, 6, 12],\n [8, -10, 2, 3, 2, 6],\n [6, -2, 3, -4, 2, 4],\n [-6, 6, 2, 2, -11, 8],\n [0, 12, 6, 4, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[10, -8, 4, -6, -3, 2],\n [-8, -14, -15, -6, 4, 0],\n [4, -15, -4, 1, -2, 2],\n [-6, -6, 1, 7, 8, -6],\n [-3, 4, -2, 8, 6, 0],\n [2, 0, 2, -6, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[6, 10, -12, -4, 4, -1],\n [10, 0, 6, 2, -8, 14],\n [-12, 6, -10, -1, -6, -6],\n [-4, 2, -1, -5, 10, 7],\n [4, -8, -6, 10, 9, -8],\n [-1, 14, -6, 7, -8, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[10, -5, -14, -2, -4, 14],\n [0, -4, 10, -4, -15, -3],\n [0, 0, 14, -14, -4, 10],\n [0, 0, 0, -12, -8, -14],\n [0, 0, 0, 0, -3, 7],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
47
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[4, 2, -8, -12, 6, -2],\n [2, -14, -8, 2, 7, 3],\n [-8, -8, 13, 0, -2, -6],\n [-12, 2, 0, -4, 4, 8],\n [6, 7, -2, 4, -8, 1],\n [-2, 3, -6, 8, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-5, -11, 0, -9, 11, -11],\n [0, -1, -13, 10, -11, 7],\n [0, 0, -7, -1, -13, 13],\n [0, 0, 0, 5, -8, 5],\n [0, 0, 0, 0, -6, 8],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-6, -4, -10, -4, 7, -2],\n [0, -7, -6, 10, 1, 1],\n [0, 0, 15, 3, -15, -4],\n [0, 0, 0, -3, -14, -6],\n [0, 0, 0, 0, 2, -11],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
47
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[-10, 0, 12, 4, -6, 8],\n [0, 15, -4, -2, -9, -2],\n [12, -4, 12, 2, 0, 0],\n [4, -2, 2, -8, -7, 9],\n [-6, -9, 0, -7, 0, 1],\n [8, -2, 0, 9, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[14, -9, 4, 8, 7, -9],\n [0, -15, 10, -10, -10, 6],\n [0, 0, 6, -4, -6, 7],\n [0, 0, 0, 1, 3, 2],\n [0, 0, 0, 0, 8, -8],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
58
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-9, 10, -2, 2, 6, 12],\n [10, 9, -1, 3, 2, -8],\n [-2, -1, -2, 9, -2, -7],\n [2, 3, 9, -5, 10, -14],\n [6, 2, -2, 10, 7, 9],\n [12, -8, -7, -14, 9, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
34
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[2, -1, -15, -11, -14, 4],\n [0, 3, 2, 13, 6, 2],\n [0, 0, 8, -8, 13, 14],\n [0, 0, 0, 7, 4, 1],\n [0, 0, 0, 0, -12, -15],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[3, 2, -11, 14, 3, 10],\n [0, 11, 6, 0, -15, -4],\n [0, 0, 5, 9, -8, 2],\n [0, 0, 0, 10, 14, 6],\n [0, 0, 0, 0, 10, -8],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-5, 1, 11, -3, -3, -9],\n [1, -4, -2, 14, -11, -2],\n [11, -2, 8, 4, -2, 2],\n [-3, 14, 4, -7, -4, -4],\n [-3, -11, -2, -4, 4, -2],\n [-9, -2, 2, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
78
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[8, 15, -12, -10, 4, -3],\n [15, -1, -6, -2, 3, 0],\n [-12, -6, -5, 4, 10, 6],\n [-10, -2, 4, 5, -4, 6],\n [4, 3, 10, -4, -8, 5],\n [-3, 0, 6, 6, 5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-12, 0, -8, 10, -4, -4],\n [0, -4, 4, 8, -6, 0],\n [-8, 4, -7, 4, -12, 8],\n [10, 8, 4, 8, -8, -6],\n [-4, -6, -12, -8, -9, -6],\n [-4, 0, 8, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
95
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-10, -10, 7, -6, -10, 8],\n [-10, -8, -6, 4, 4, 1],\n [7, -6, -10, 1, -4, 4],\n [-6, 4, 1, -6, -2, -4],\n [-10, 4, -4, -2, -8, -12],\n [8, 1, 4, -4, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
90
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-13, -7, 13, 5, 2, -5],\n [0, 14, 15, 9, 7, -14],\n [0, 0, -12, 13, -7, 15],\n [0, 0, 0, 12, -6, 0],\n [0, 0, 0, 0, -6, -15],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[8, -2, -7, 0, 10, -4],\n [-2, 1, 8, -12, 11, 4],\n [-7, 8, 11, -3, -6, -7],\n [0, -12, -3, 8, 4, -4],\n [10, 11, -6, 4, -1, 0],\n [-4, 4, -7, -4, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[1, 4, 3, 3, 5, 7],\n [4, -1, 12, -5, -2, 5],\n [3, 12, -12, -2, 6, 8],\n [3, -5, -2, 2, 6, 11],\n [5, -2, 6, 6, 8, -2],\n [7, 5, 8, 11, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[5, -4, -2, 10, 4, -6],\n [-4, 5, 1, -6, -1, 0],\n [-2, 1, 14, -8, -4, -8],\n [10, -6, -8, 4, 6, -6],\n [4, -1, -4, 6, -4, -3],\n [-6, 0, -8, -6, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
26
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-6, 2, -2, -6, -8, 2],\n [2, -6, 0, -6, 6, 8],\n [-2, 0, -8, -5, 0, 7],\n [-6, -6, -5, 14, 8, -4],\n [-8, 6, 0, 8, 9, 2],\n [2, 8, 7, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
75
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[15, 0, -6, -4, -5, 2],\n [0, 8, -14, 12, 12, 0],\n [-6, -14, 10, -10, 4, 10],\n [-4, 12, -10, -9, 5, 0],\n [-5, 12, 4, 5, 8, 2],\n [2, 0, 10, 0, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[12, -10, 2, -2, 0, -8],\n [-10, 9, 0, -5, -4, -5],\n [2, 0, -6, 7, -4, 0],\n [-2, -5, 7, 15, 0, -2],\n [0, -4, -4, 0, -4, -2],\n [-8, -5, 0, -2, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[-10, 3, 5, -3, 1, 7],\n [0, 1, 13, -14, 3, 3],\n [0, 0, 6, 15, -6, -6],\n [0, 0, 0, 1, 11, -1],\n [0, 0, 0, 0, 3, 1],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the sum of absolute values of all eigenvalues:\n[[-9, 1, -9, -12, -8, -3],\n [0, -10, 9, -11, 14, -4],\n [0, 0, 13, -7, -12, 3],\n [0, 0, 0, 2, -6, 9],\n [0, 0, 0, 0, 14, 8],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
49
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[12, 3, -2, -2, 0, 12],\n [3, -13, 5, 2, 8, 4],\n [-2, 5, -15, 2, 4, 0],\n [-2, 2, 2, 11, 6, 12],\n [0, 8, 4, 6, 0, -6],\n [12, 4, 0, 12, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
93
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[13, 8, -7, -5, -2, 10],\n [8, -14, 1, -10, 0, 10],\n [-7, 1, 15, 4, 12, 2],\n [-5, -10, 4, 3, 0, -1],\n [-2, 0, 12, 0, -12, -12],\n [10, 10, 2, -1, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
97
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-2, 10, 12, 0, 6, 2],\n [10, -10, -4, -12, -2, 11],\n [12, -4, -9, 2, 3, -4],\n [0, -12, 2, 2, -2, 0],\n [6, -2, 3, -2, -14, -2],\n [2, 11, -4, 0, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
MATH
|
[
{
"content": "What is the largest eigenvalue by absolute value for the following matrix?\n[[-9, 14, -7, 15, 3, 12],\n [0, 7, -9, 7, -14, -10],\n [0, 0, -3, 10, 3, 14],\n [0, 0, 0, -2, -10, 2],\n [0, 0, 0, 0, 6, 6],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
MATH
|
[
{
"content": "Determine the largest eigenvalue by absolute value of the matrix:\n[[0, 1, -9, -3, 8, -14],\n [0, -6, -9, 8, 1, 4],\n [0, 0, -11, -6, -7, 11],\n [0, 0, 0, 8, -10, -12],\n [0, 0, 0, 0, -12, 9],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "Find the eigenvalues of the matrix and calculate the largest eigenvalue by absolute value:\n[[8, -3, -2, -11, 4, -8],\n [-3, -2, -6, 10, -8, 4],\n [-2, -6, 1, -8, 6, -10],\n [-11, 10, -8, 4, -2, -4],\n [4, -8, 6, -2, 6, 6],\n [-8, 4, -10, -4, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
28
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[-4, 2, -7, 5, -10, 0],\n [2, -7, 8, 2, 4, -5],\n [-7, 8, -6, -9, 2, -7],\n [5, 2, -9, -13, 0, 6],\n [-10, 4, 2, 0, -9, -4],\n [0, -5, -7, 6, -4, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
23
|
MATH
|
[
{
"content": "What is the sum of absolute values of all eigenvalues for the following matrix?\n[[-8, 0, -10, -6, -1, 2],\n [0, -10, -2, 8, 8, 6],\n [-10, -2, 0, 3, -3, 0],\n [-6, 8, 3, -5, -10, 6],\n [-1, 8, -3, -10, -10, -1],\n [2, 6, 0, 6, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
71
|
MATH
|
[
{
"content": "Determine the sum of absolute values of all eigenvalues of the matrix:\n[[13, -1, -10, 8, 0, -12],\n [-1, 2, 2, -8, -4, -6],\n [-10, 2, 5, -6, 10, -6],\n [8, -8, -6, -6, -2, 6],\n [0, -4, 10, -2, 0, -4],\n [-12, -6, -6, 6, -4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
91
|
MATH
|
[
{
"content": "Calculate the sum of absolute values of all eigenvalues for the matrix:\n[[-3, 2, 6, 10, -10, 3],\n [2, 5, 1, -6, -4, 9],\n [6, 1, 14, 2, 2, 6],\n [10, -6, 2, -1, 8, 13],\n [-10, -4, 2, 8, -14, 4],\n [3, 9, 6, 13, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
89
|
MATH
|
[
{
"content": "Calculate the largest eigenvalue by absolute value for the matrix:\n[[13, -3, 4, -2, -6, 1],\n [-3, 14, -14, 6, 12, -6],\n [4, -14, -10, 0, -8, 13],\n [-2, 6, 0, 15, -8, -8],\n [-6, 12, -8, -8, -1, -6],\n [1, -6, 13, -8, -6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
39
|
MATH
|
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